How do I prove the linear independence of the standard basis vectors? My book is helpful by giving the definition of linear independence and a couple examples, but never once shows how to prove that they are linearly independent.(adsbygoogle = window.adsbygoogle || []).push({});

I know that the list of standard basis vectors is linearly independent if:

The only choice of a_1, a_2, ... a_m that makes a_1v_1+a_2v_2+...+a_mv_m=0 is a_1=a_2=...=a_m=0.

But i don't know where to go from there .. any help would be appreciated

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# Linear independence of basis vectors

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